On the front conditions for gravity currents in channels of general cross-section

We consider the propagation of a high-Reynolds-number gravity current in a horizontal channel with general cross-section whose width is \(f(z), 0 \le z\le H\), and the gravity acceleration g acts in \(-z\) direction. (The classical rectangular cross-section is covered by the particular case \(f(z) =\) const.) We assume a two-layer system of homogeneous fluids of constant densities \(\rho _{c}\) (current, of height \(h < H \)) and smaller \(\rho _{a}\) (ambient, filling the remaining part of the channel). We focus attention on the calculation and assessment of the nose Froude-number condition \(Fr = U/(g' h)^{1/2}\); here U is the speed of propagation of the current and \(g' = (\rho _{c}/\rho _{a}-1) g\) is the reduced gravity. We first revisit the steady-state current, and derive compact insightful expressions of Fr and energy dissipation as a function of \(\varphi \) (\(=\) area fraction occupied by the current in the cross-section). We show that the head loss \(\delta _0\) on the stagnation line is formally a degree of freedom in the determination of \(Fr(\varphi )\), and we clarify the strong connections with the head loss \(\delta \) in the ambient fluid, and with the overall rate of dissipation \(\dot{{\mathcal{D}}}\). We demonstrate that the closure \(\delta _0 = 0\) [suggested by Benjamin (J Fluid Mech 31, 209–248, 1968) for the rectangular cross-section] produces in general the smallest Fr for a given \(\varphi \); the results are valid for a significant range \([0, \varphi _{\max }]\), in which the current is dissipative, except for the point \(\varphi _{\max }\) where \(\delta = \dot{{\mathcal{D}}} = 0\). We show that imposing the closure \(\delta = \dot{{\mathcal{D}}} = 0\), which corresponds to an energy-conserving or non-dissipative current, produces in general unacceptable restrictions of the range of validity, and large values of Fr; in particular, deep currents (\(\varphi < 0.3\) say) must be excluded because they are inherently dissipative. On the other hand, the compromise closure \(\delta (\varphi ) =\delta _0(\varphi )\) produces the simple \(Fr(\varphi ) = \sqrt{2}(1 - \varphi )\) formula whose values and dissipation properties are very close, and the range of validity is identical, to these obtained with Benjamin’s closure (moreover, we show that this corresponds to circulation-conservation solutions). The results are illustrated for practical cross-section geometries (rectangle, \(\Delta \) and \(\nabla \) triangle, circle, and the general power-law \(f(z) = b z ^\alpha \) (\(b>0, \alpha \ge 0, 0< z \le H\)). Next, we investigate the connection of the steady-state results with the time-dependent current, and show that in a lock-released current the rate of dissipation of the system is equal to, or larger than, that obtained for Fr corresponding to the conditions at the nose of the current. The results and insights of this study cover a wide range of cross-section geometry and apply to both Boussinesq and non-Boussinesq systems; they reveal a remarkable robustness of Fr as a function of \(\varphi \).     

Bayesian analysis of Jolly-Seber type models

We propose the use of finite mixtures of continuous distributions in modelling the process by which new individuals, that arrive in groups, become part of a wildlife population. We demonstrate this approach using a data set of migrating semipalmated sandpipers (Calidris pussila) for which we extend existing stopover models to allow for individuals to have different behaviour in terms of their stopover duration at the site. We demonstrate the use of reversible jump MCMC methods to derive posterior distributions for the model parameters and the models, simultaneously. The algorithm moves between models with different numbers of arrival groups as well as between models with different numbers of behavioural groups. The approach is shown to provide new ecological insights about the stopover behaviour of semipalmated sandpipers but is generally applicable to any population in which animals arrive in groups and potentially exhibit heterogeneity in terms of one or more other processes.     

Estimating abundance: a non parametric mark recapture approach for open and closed systems

We present a novel, non-parametric, frequentist approach for capture-recapture data based on a ratio estimator, which offers several advantages. First, as a non-parametric model, it does not require a known underlying distribution for parameters nor the associated assumptions, eliminating the need for post-hoc corrections or additional modeling to account for heterogeneity and other violated assumptions. Second, the model explicitly deals with dependence of trials by considering trials to be dependent; therefore, cluster sampling is handled naturally and additional adjustments are not necessary. Third, it accounts for ordering, utilizing the fact that a system with a small population will have a greater frequency of recaptures “early” in the survey work compared to an identical system with a larger population. We provide mathematical proof that our estimator attains asymptotic minimum variance under open systems. We apply the model to a data set of bottlenose dolphins (Tursiops truncatus) and compare results to those from classic closed models. We show that the model has an impressive rate of convergence and demonstrate that there’s an inverse relationship between population size and the proportion of the population that need to be sampled, while achieving the same degree of accuracy for abundance estimates. The model is flexible and can apply to ecological situations as well as other situations that lend themselves to capture recapture sampling.     

Sparse PCA and investigation of multi-elements compositional repositories: theory and applications

The geochemistry of floodplain sediments is fundamental to monitor environmental changes and to quantify their contribution to natural and anthropic processes. A floodplain sediment composition is a vector of positive elements which sum to a fixed constant. The analysis of high-dimensional compositions requires methods that produce results involving only a small portion of the original variables. On the other hand, the analysis must take into account the additional constraints specific to compositions. With the purpose of studying these problems, a new procedure for sparse PCA is proposed on European floodplain sediment samples.     

Analysis and prediction of $$\mathrm{PM}_{10}$$ concentration levels in Tunisia using statistical learning approaches

Over the past years, the health impact of airborne particulate matter \(\mathrm{PM}_{10}\) has become a very topical subject. Thereby, a lot of research effort in the environmental sciences goes towards the modeling and the prediction of ambient \(\mathrm{PM}_{10}\) concentrations. In this paper, we are interested in the statistical classification of the daily mean \(\mathrm{PM}_{10}\) concentration in Tunisia according to the authority regulation. We consider two monitoring stations: a big industrial station and a traffic station. The main goal of this work is to determine the pertinent predictors of \(\mathrm{PM}_{10}\) concentration within a nonlinear multiclass framework. To do this, we used two popular statistical learning methods; the support vector machines (SVM) and the random forests (RF). The statistical results obtained on the real datasets, show that RF outperform SVM for the purpose of variable selection even with a reduced number of observations compared to the number of explicative variables. It was also demonstrated that the \(\mathrm{PM}_{10}\) concentration measured yesterday is the most relevant predictor of its present-day value. Moreover, we found that the more delayed values of \(\mathrm{PM}_{10}\) concentration may be crucial to get an accurate prediction.     

Vertical oil dispersion profile under non-breaking regular waves

An experimental program was conducted to investigate vertical oil dispersion of surface oil spills under non-breaking regular waves. The variation in oil concentration caused by oil dispersion in a water column was studied to determine the vertical oil dispersion profile. The experiments were performed using different waves characteristics for different volumes of oil spill to evaluate the variation in oil concentration at three depths at two sampling stations. The correlations between oil concentration and the main parameters of wave characteristics, oil spill volume, sampling depth, and distance of sampling stations to spill location were assessed. The results revealed that the trend of variation in oil concentration versus wave steepness is linear. The results obtained from experimental measurements indicated that the oil concentrations at mid-depth were 44–77 % and the concentrations near the flume bed were 12–33 % of the concentration near the water surface.     

Simulations of the flow in the Mahakam river–lake–delta system,Indonesia

Large rivers often present a river–lake–delta system, with a wide range of temporal and spatial scales of the flow due to the combined effects of human activities and various natural factors, e.g., river discharge, tides, climatic variability, droughts, floods. Numerical models that allow for simulating the flow in these river–lake–delta systems are essential to study them and predict their evolution under the impact of various forcings. This is because they provide information that cannot be easily measured with sufficient temporal and spatial detail. In this study, we combine one-dimensional sectional-averaged (1D) and two-dimensional depth-averaged (2D) models, in the framework of the finite element model SLIM, to simulate the flow in the Mahakam river–lake–delta system (Indonesia). The 1D model representing the Mahakam River and four tributaries is coupled to the 2D unstructured mesh model implemented on the Mahakam Delta, the adjacent Makassar Strait, and three lakes in the central part of the river catchment. Using observations of water elevation at five stations, the bottom friction for river and tributaries, lakes, delta, and adjacent coastal zone is calibrated. Next, the model is validated using another period of observations of water elevation, flow velocity, and water discharge at various stations. Several criteria are implemented to assess the quality of the simulations, and a good agreement between simulations and observations is achieved in both calibration and validation stages. Different aspects of the flow, i.e., the division of water at two bifurcations in the delta, the effects of the lakes on the flow in the lower part of the system, the area of tidal propagation, are also quantified and discussed.     

Photochemical indicators of ozone sensitivity: application in the Pearl River Delta,China

Surface O₃ production has a highly nonlinear relationship with its precursors. The spatial and temporal heterogeneity of O₃-NO _x -VOC-sensitivity regimes complicates the control-decision making. In this paper, the indicator method was used to establish the relationship between O₃ sensitivity and assessment indicators. Six popular ratios indicating ozone-precursor sensitivity, HCHO/NO _y , H₂O₂/ HNO₃, O₃/NO _y , O₃/NO _z , O₃/HNO₃, and H₂O₂/NO _z , were evaluated based on the distribution of NO_x- and VOC-sensitive regimes. WRF-Chem was used to study a serious ozone episode in fall over the Pearl River Delta (PRD). It was found that the south-west of the PRD is characterized by a VOCsensitive regime, while its north-east is NO _x -sensitive, with a sharp transition area between the two regimes. All indicators produced good representations of the elevated ozone hours in the episode on 6 November 2009, with H₂O₂/HNO₃ being the best indicator. The threshold sensitivity levels for HCHO/NO_y, H₂O₂/HNO₃, O₃/NO _y , O₃/NO _z , O₃/HNO₃, and H₂O₂/NO _z were estimated to be 0.41, 0.55, 10.2, 14.0, 19.1, and 0.38, respectively. Threshold intervals for the indicators H₂O₂/HNO₃, O₃/NO _y , O₃/NO _z , O₃/HNO₃, and H₂O₂/NO _z were able to identify more than 95% of VOC- and NO _x -sensitive grids. The ozone episode on 16 November 16 2008 was used to independently verify the results, and it was found that only H₂O₂/HNO₃ and H₂O₂/NO _z were able to differentiate the ozone sensitivity regime well. Hence, these two ratios are suggested as the most appropriate indicators for identifying fall ozone sensitivity in the PRD. Since the species used for indicators have seasonal variation, the utility of those indicators for other seasons should be investigated in the future work.

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Improving simulations of sulfate aerosols during winter haze over Northern China: the impacts of heterogeneous oxidation by NO<Subscript>2</Subscript>

We implemented the online coupled WRF-Chem model to reproduce the 2013 January haze event in North China, and evaluated simulated meteorological and chemical fields using multiple observations. The comparisons suggest that temperature and relative humidity (RH) were simulated well (mean biases are–0.2K and 2.7%, respectively), but wind speeds were overestimated (mean bias is 0.5 m?s^–1). At the Beijing station, sulfur dioxide (SO₂) concentrations were overpredicted and sulfate concentrations were largely underpredicted, which may result from uncertainties in SO₂ emissions and missing heterogeneous oxidation in current model. We conducted three parallel experiments to examine the impacts of doubling SO₂ emissions and incorporating heterogeneous oxidation of dissolved SO₂ by nitrogen dioxide (NO₂) on sulfate formation during winter haze. The results suggest that doubling SO₂ emissions do not significantly affect sulfate concentrations, but adding heterogeneous oxidation of dissolved SO₂ by NO₂ substantially improve simulations of sulfate and other inorganic aerosols. Although the enhanced SO₂ to sulfate conversion in the HetS (heterogeneous oxidation by NO₂) case reduces SO₂ concentrations, it is still largely overestimated by the model, indicating the overestimations of SO₂ concentrations in the North China Plain (NCP) are mostly due to errors in SO₂ emission inventory.

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